The 19-year-old Harper, one of the hottest prospects in Major League Baseball, record the sixth homer of his career with a 420-feet blast over center field in the fourth inning.
He also hit a double in the third and a single in the sixth to finish a triple away of the cycle in his Fenway Park.
Washington starter Stephen Strasburg gave up his two runs in six innings in a season high 119 pitches. Strasburg (7-1) allowed two runs in the second inning but shut down the Red Sox the rest of the way with 13 strikeouts.
"It was good to see all the young guys here rise and know that you're playing in one of the most historic ballparks in the game and have the sellout crowd like that," Strasburg told reporters.
Boston slugger Adrian Gonzalez hit his 200th career homer off Washington's Ross Detwiler.
The result allowed the Nationals (33-23) to stay ahead of the Atlanta Braves in the National League East while the Red Sox (29-29) remained rooted to the bottom of the American League East.
(Reporting by Julian Linden in New York; Editing by John O'Brien)
